Masuda: When I watched the lectures and seminars that I taught, I got the impression that you both were very enthusiastic about your studies. What classes did you find particularly interesting?

Ito: For me, it was "Algebra I and II," where we learned about group theory and ring theory. It really felt like university-level mathematics, and I found it interesting how by learning more abstract concepts, you can understand the theorems you learned earlier as applications of more general theorems.

Nogami: That's right. I took analysis from "Analysis IA / IB" in my first year to "Analysis IV" in my third year, and because it took me a long time to understand it, I felt a greater sense of accomplishment when I finally did. Analysis deals with the concept of "infinity," which isn't covered in detail in mathematics up to high school. Everything we can see and think about is "finite," but by learning in depth about "infinity" for the first time at university, I began to enjoy thinking mathematically about what lies beyond "finite."

Masuda: Ito-san, I get the impression that you are eager to learn and that you tackle mathematics calmly, but do you ever have any difficulties studying?

Masuda: If you can stop and think about why something is the way it is, that's proof that you can read the text to a certain extent. If you just skim through it, your thoughts of "I thought I understood" will pile up, and when you look back, you'll realize that you didn't understand anything. Looking back on your life, Mr. Nogami, have you ever had any difficulties?

Similar to what Nogami Ito said, if you don't understand the meaning of the definition in the first place, you may not understand the theorems and propositions that follow. You have to start by understanding the definition, but I often have trouble with that. As Professor Masuda does in his algebra lectures, I try to be conscious of writing down examples that come to mind and finding patterns. By repeating this kind of learning, I feel that when I'm faced with a problem I don't understand, I rarely find myself saying, "I have no idea what to do at all," and I'm starting to come up with my own methods for solving it.

Masuda: Understanding mathematics doesn't happen overnight, but the pleasure you feel when you finally understand something after thinking about it is an experience that can't be replaced by anything else. When you don't understand something, I hope you'll persevere and continue to enjoy learning mathematics, with the attitude of being resigned to the fact that "it would be boring if everything was immediately understandable."

Masuda: The curriculum of our department places emphasis on acquiring not only basic knowledge and problem-solving skills in mathematics and mathematical sciences, but also communication and presentation skills to convey what you have understood to others. Until the second year, the curriculum aims to enable students to write mathematical answers in a way that others can understand, and from the third year onwards, the curriculum also aims to enable students to speak while writing so that the content of mathematics can be conveyed to others. A major feature of our department is the richness of our seminar courses.

Among the Ito seminars, the third-year "Specialized Mathematics Seminar I & II" was the class in which I took the most initiative. This class was two consecutive periods, and in the first half, students practiced problems based on subjects they had already learned, writing the answers they had solved on the board and presenting them. The second half was in the form of a text seminar, with each student taking charge of a designated section of a text and explaining the content in an easy-to-understand manner for everyone, also writing on the board. Through the exercises, I was able to review in detail the various subjects I had learned in my first and second years, and I think I also acquired the ability to communicate with others.

Masuda Mathematics books often omit things that are obvious to the author, and it often takes students several hours to read one line. We ask students to clarify the omitted parts before making their presentations. One of the shortcuts to deepening your understanding of mathematics is to explain it to others while writing on the board. Whether it is "study" to acquire known facts or "research" to explore unknown themes, the effect of trying to explain it to others is enormous. This seminar format becomes the standard style for fourth-year and graduate students, so the third-year specialized mathematics seminar is a kind of warm-up exercise for that.

Nogami: Mathematics Seminar is a class that students have no choice but to tackle independently. In a normal lecture, even if there is something in the text that I don't understand, I can understand it by listening to the teacher's explanation. But in Mathematics Seminar, I have to read the book by myself and understand it more than others in order to give a presentation. If there was something I didn't understand, I would talk to my friends, and I would spend a lot of time preparing before going to class.

After graduating, Nogami plans to go on to graduate school at this university. He wants to learn more about mathematics, and because he loves mathematics, he wants to work in a profession that has some connection to it. That is the reason for his decision to go on to graduate school.

Masuda: The number of students going on to graduate school has increased significantly compared to when I was in the Department of Physics and Mathematics, and about 30% of the first batch of students go on to graduate school. For students who wish to continue on to graduate school within the university, there is the "Special Grant Scholarship Graduate School of Science and Engineering," which provides full or half of tuition fees to top-achieving students, so I think this system also encourages students to continue on to graduate school.

Nogami: I also plan to take advantage of this scholarship. If it is fully funded, it will be possible to go to graduate school at a lower tuition than at a national university, so many of my friends have decided to go to graduate school because of the scholarship.

Ito: I'm still a third-year student, but I'm thinking of going on to graduate school, so the existence of this scholarship is appealing. Only students with high grades can apply for this scholarship, so it motivates me to study hard in order to qualify to apply.

Masuda: I hope that when you both go on to graduate school, you will be even more enthusiastic about mathematics than you have been until now. In the master's course, you will gradually transition from "study" to "research." Research, which involves exploring unknown themes on your own, has its challenges that are different from those of studying, but I hope that you will enjoy mathematics itself, including the situations where you "don't understand."

Besides going on to graduate school, many Masuda graduates become junior high and high school mathematics teachers. If they get a job at a general company, the most common jobs are systems engineers (SE) and finance-related jobs. There may not be many people who get a job where they can directly use the mathematics they learned at university. For such graduates, what is truly useful when they enter society is not the knowledge of mathematics itself, but the thinking and communication skills they have cultivated while studying mathematics. When there is a problem, the ability to go back to the root of the problem, understand it step by step, and then speak in a way that properly conveys what you have understood is important no matter what profession you choose. That is why our department has organized its curriculum with a focus on training these skills.

Ito: Through the class on communicating what I have understood to others, I realized that I am biased when talking to others about what I am good at or what I like. There are times when I end up leaving the other person behind without realizing it, so I will be conscious of that and work on improving.

Nogami: Like Mr. Ito, I also experienced in my third year specialized mathematics seminar that if you talk assuming that your own knowledge is the premise, there will be a misunderstanding. Since I became a fourth year student, I have assumed that the other person does not have any prior knowledge, so I try to make presentations that include premise knowledge and concrete examples, and also explain the process by which I understood it, so that everyone can understand it on the spot.

I hope that by studying along the Masuda curriculum, students will naturally acquire the communication skills to convey their thoughts and facts to others in an easy-to-understand manner, and the habit of going back to basics to think. The good thing about Department of Mathematical Sciences is that if you study hard for four years, you will acquire logical thinking and communication skills that can be used anywhere. I think that the two students enrolled because they liked math, but if you like math up to high school, I hope you will enjoy learning math in this department as an extension of that. Also, even if the style of math up to high school, where you solve given problems within a certain time, does not suit you, in university math it is important to think carefully, so if you like to take your time to think, I would definitely recommend you to come to our department.

In the field of mathematical sciences, cutting-edge research is being actively conducted in fields such as representation theory, which mathematically explores the symmetry of various objects and phenomena; nonlinear integrable systems, which are deeply related to mathematical physics and various fields of mathematics; biomathematics, which uses mathematical models to elucidate complex phenomena in the biological world; financial engineering, which uses knowledge from mathematical science to address problems in the fields of economics and finance; dynamical systems theory, which studies chaotic phenomena that appear in the movement of celestial bodies and the weather; and probability theory, which mathematically deals with uncertain phenomena and random events.